Answer:
108 th term is zero
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 99 and a₉₉ = 9 then
a₁ + 8d = 99 → (1)
a₁ + 98d = 9 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 90d = - 90
90d = - 90 ( divide both sides by 90 )
d = - 1
Substitute d = - 1 into (1) for value of a₁
a₁ + 8(- 1) = 99
a₁ - 8 = 99 ( add 8 to both sides )
a₁ = 107
Then
107 - (n - 1) = 0
107 - n + 1 = 0
- n + 108 = 0 ( subtract 108 from both sides )
- n = - 108 ( multiply both sides by - 1 )
n = 108
The 108th term is zero
Answer:
Dimensions = 7 cm by 20 cm.
Step-by-step explanation:
Let the length and width of the rectangle be L & W respectively.
Given the following data;
Area of rectangle = 140 cm²
L = W - 13
To find the dimensions of the rectangle;
The area of rectangle = L * W
Substituting into the above formula, we have;
140 = L * W
140 = (W - 13) * W
140 = W² - 13W
W² - 13W - 140 = 0
Solving the quadratic equation using factorization method;
Factors are -20 and 7
W² - 20W + 7W - 140 = 0
W(W - 20) + 7(W - 20) = 0
(W - 20)(W + 7) = 0
W - 20 = 0
W = 20
W + 7 = 0
W = -7
Thus, W = 20 or -7
But the width has to be positive, W = 20 centimeters.
Next, to find the length of rectangle
L = W - 13
L = 20 - 13
L = 7 centimeters.
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Answer:
8
Step-by-step explanation:
Using the Heron's formula we can find that the total area of the triangle is 84 inches.
Then, to find the height of the triangle, you have to multiply the area by 2 since the formula for the area of a triangle is (h*b)/2
Now, when we multiply 84 and 2 we get 168, so you have to divide 168 by 21 to find 8.